M. I. Pupin—Studies in the Electro-magnetic Theory. 327 
electric field is proportional to the rate of variation of the 
magnetic flux through any surface bounded by this circuit. 
: Second law :—An electric current induces a field of magnetic 
orce : ; : : : 
The magnetomotive force around any simple circuit of this 
induced magnetic field is proportional to the current passing 
through any surface bounded by this circuit. 
For the sake of brevity the factors of proportionality are 
not explicitly mentioned. It is well to observe, however, that 
they are numerical and that by a suitable selection of electric 
units they could be made unity in each ease. 
There is evidently a considerable formal resemblance between 
these two experimental laws when they are stated in the form 
in which they have just been stated. This formal resemblance 
can be carried considerably further without departing from the 
views of pre-Maxwellian electric theories. All that is needed 
is a simple adjustment of the electric terminology of the pre- 
Maxwellian period. This is the step which is now in order. 
It leads along the shortest path from old theories to Maxwell’s 
electro-magnetic theory. 
Consider two electric conductors A and B, insulated from 
each other, one charged with a certain quantity of positive 
electricity and the other with an equal charge of negative elec- 
tricity. Consider now a surface surrounding any one of these 
two conductors. The total electric flux through this surface is 
numerically equal to the total quantity of electricity enclosed 
by the surface. Hence it is also equal to the total integral 
electrie current which would be obtained if the total positive 
charge were carried across this surface to the negatively charged 
conductor and thus the two conductors reduced to their neutral 
state. We can speak, therefore, of a total electric flux across 
a surface as of a fictitious integral current through this sur- 
face. Wecan speak of it also as of a total electric displace- 
ment in the sense that if the two conductors are neutral and a 
certain quantity of positive or negative electrification is trans- 
ferred from one to the other and therefore displaced from one side 
of the bounding surface to the other we shall have a total electric 
flux across this surface numerically equal to the total electric 
displacement across the same surface. With this mental reser- 
vation, namely, that we are using certain terms in their figura- 
tive sense only, we can always employ the expressions “ total 
electric flux,’ “total integral current,” and “ total electric dis- 
placement” as synonymous terms without departing from 
the views of pre-Maxwellian theories. 
So far we have not restricted the fictitious total integral 
current or displacement to any particular paths. That shall 
be done now. 
